标题： 纸折叠模型用于CAR代数 显示英文标题

标题： Paper-folding models for the CAR algebra

摘要： 我们证明CAR代数具有一个Cantor谱的C*-对角，该对角不共轭于标准的AF对角。 我们通过C*-代数的分类理论得到这一结果，该对角是通过将CAR代数视为Cantor空间上自由极小作用的交叉积而得到的，其中作用群是局部有限群与无限二面体群的乘积。 构造的主要成分是一个与众所周知的正则折纸序列相关的二进制子移位。 此外，我们证明CAR代数实际上 admits 可数多个两两不共轭的Cantor谱对角，这些对角通过Li、Liao和第二作者定义的对角维数的不同值来区分。 显示英文摘要

摘要： We show that the CAR algebra admits a Cantor spectrum C*-diagonal that is not conjugate to the standard AF diagonal. We obtain this by classification theory of C*-algebras, and the diagonal arises by realising the CAR algebra as the crossed product of a free minimal action on the Cantor space, where the acting group is the product of a locally finite group with the infinite dihedral group. The main ingredient in the construction is a binary subshift associated to the well-known regular paper-folding sequence. Moreover, we show that the CAR algebra in fact admits countably many, pairwise non-conjugate, Cantor spectrum diagonals which are distinguished by the different values of their diagonal dimension, as defined by Li, Liao and the second named author.